# Effect of the Anomalous Diffusion of Fluctuating Cooper Pairs in the Density of States of Superconducting NbN Thin Films

## TL;DR

This paper investigates how anomalous diffusion of fluctuating Cooper pairs in disordered NbN thin films affects the electron density of states above the critical temperature, revealing pseudogap-like behavior without stable preformed pairs.

## Contribution

It introduces a model assuming anomalous diffusive behavior of Cooper pairs and calculates its impact on the density of states, bridging the bosonic and fermionic paradigms in superconducting-insulator transitions.

## Key findings

- Density of states is suppressed above $T_c$.
- Behavior resembles a pseudogap.
- No stable preformed pairs are needed.

## Abstract

Recent scanning tunnelling microscopy experiments in NbN thin disordered superconducting films found an emergent inhomogeneity at the scale of tens of nanometers. This inhomogeneity is mirrored by an apparent dimensional crossover in the paraconductivity measured in transport above the superconducting critical temperature $T_c$. This behavior was interpreted in terms of an anomalous diffusion of fluctuating Cooper pairs, that display a {\em quasi-confinement} (i.e., a slowing down of their diffusive dynamics) on length scales shorter than the inhomogeneity identified by tunnelling experiments. Here we assume this anomalous diffusive behavior of fluctuating Cooper pairs and calculate the effect of these fluctuations on the electron density of states above $T_c$. We find that the density of states is substantially suppressed up to temperatures well above $T_c$. This behavior, which is closely reminiscent of a pseudogap, only arises from the anomalous diffusion of fluctuating Cooper pairs in the absence of stable preformed pairs, setting the stage for an intermediate behavior between the two common paradigms in the superconducting-insulator transition, namely the localisation of Cooper pairs (the so-called bosonic scenario) and the breaking of Cooper pairs into unpaired electrons due to strong disorder (the so-called fermionic scenario).